Pretty fun! There's definitely room to play around with this concept. I think there could be a good amount of depth here if you developed it further. The standout puzzles are the ones where it's advantageous to keep the dice around longer to go for a "chain reaction" of solving dice. I also like how you solved the problem of displaying the non-visbile sides of the dice. It works well.
In a sufficiently big room (like the last one), you run into as problem where I can kind of just randomly roll around until the numbers happen to align, though (I did end up beating level 8 in 16 moves, which I thought was pretty good!). Maybe that could be solved by having a "health meter" of some kind that depletes a little on each roll.
I would also say that, for the music, probably would just be better off without it rather than a simple two second loop. It grates after a while.