It's a good question. By cause and effect we mean A happened then B happened because A happened. With quantum mechanics (as we understand it today) the link between A and B is less clear cut because of the probabilistic nature of quantum results. It's worth digging into that nature ...
If A is 'I threw a dice' and B is 'it was a six', then we are simplifying the chain of cause and effect. The dice didn't land with six facing upwards just because I threw it- there were lots of other factors at play, such as its linear and angular momentum when it left my hand, the interaction between the dice and the air, the exact height and position of my hand relative to the surface upon which the dice was dropped etc etc etc. Were we able to know all those factors, we might be able to work out for certain that the dice was going to land as a six, so the probabilistic nature is really a result of our inability to see and follow a more detailed chain of cause and effect. With quantum theory we are in a somewhat different position. We can calculate and assign probabilities to quantum interactions, but as yet nobody has been able to suggest what the underlying chain of events might be that cause one of the outcomes to occur. Crucially, indeed, there are theorems that prove that the probabilities associated with quantum effects cannot be accounted for by some underlying chain of events in the way that the dice roll can be, unless you abandon the idea that instantaneous action at a distance is unphysical.
So, whereas with the dice we know the outcome must be a number between one and six and we could in principle figure our which if we could follow the underlying deterministic chain of events closely, with quantum mechanics we are currently forced to conclude that in principle there cannot be an underlying chain of events. We can say the dice landed on a six because of n factors, but we can't say the same about quantum outcomes- we can't bridge the gap between 'this happened' and 'then that happened' in a way that allows us to identify a chain of cause and effect that makes sense from a common sense perspective.
To put it another way, if I knew all of the starting conditions in sufficient detail, I could figure out that your dice throw would land on a six. With quantum mechanics you cannot, in principle, figure things out with that kind of certainty.
That said, however, at a macroscopic level most quantum indeterminacy disappears, so the principle of sufficient reason holds good in any domain in which you can meaningfully apply classical physics.