As other answers have indicated, the chance that Marx knew about Nietzsche is virtually zero. Nietzche's most significant works were published after Marx's death. The Gay Science was published in the year before Marx's death but I can find no evidence to suggest that he might have known about it.
@Conifold correctly states that we have no evidence that Nietzsche read Marx directly. On the other hand, Thomas Brobjer shows that Nietzsche probably knew Marx's name (he underlined it in a book) and he certainly knew something about Marxist thought. He seems to have read a number of books (written by Lange, Dühring, Frantz, Schäffle, Bebel and Jacoby) that quote or discuss Marx at length.
Brobjer's deals only briefly with what Nietzche may have actually thought about Marx and Marxism:
The reason for the absence of discussions of Marx, and of themes
central to Marxism, in Nietzsche’s writings may be due to his
general rejection of such thinking, as was the case with political
economy. It seems likely that it was natural for him to subsume such
questions into his general critique of political and economic thinking,
and even more so into his critique of socialism. Nietzsche’s critique
of Marxism can therefore only be dealt with in relation to his
critique of socialism in a wider context.
Overall it is fairly clear that Nietzsche explicitly rejected socialism and related political philosophies across several of his major works. In that way, yes, it's is difficult to reconcile Nietzsche and Marx. However there are a number of works that deal with interesting connections and parallels between their works.
Ada Albequrque de Silva focuses on their shared rejection of religion and also the distinct kinds of "redemptive" visions they each put forward.
The similarities between these two seminal thinkers are remarkable: they were contemporaries, their lives overlapping by four decades, and they both rose from privileged classes in Germany. Their concerns were strikingly similar. Each one strove to moor the human psyche in an increasingly fragmented world. To achieve this, each sublimated his early religious influences into a philosophical doctrine, emphasizing the importance of an earthly redemption over a mythical redemption in the afterlife. But there the similarities end. While the Overman attains solitary spiritual redemption, the proletariat attains redemption based on a communal harmony that provides for men both spiritually and materially. While Marx places man's salvation in the embrace of collective humanity, Nietzsche finds it in high solitude, far from the madding crowd.
Robert Miner goes a bit further to argue that some of Nietzche's later thought can be interpreted as implying a certain sympathy for socialism in the following form:
(1) In particular circumstances, when inequalities become too massive to bear, some version of socialism deserves unhesitant and energetic support; (2) one should resist the allure of becoming a partisan who sees the whole of human life as an attempt to build a new society that conforms to the socialist vision.
Overall, I would say that your question seems to be very much on track. Yes they are basically antithetical. However there is just enough common ground that a number of thinkers have brought the two in to a kind of dialogue.