Wow, what an awesome idea for the game. I got kinda stuck on the "No way out?" level. I guess there was much easier solution, but after beating that i felt like i solved a rubik's cube. This was pretty satisfying experience. But then next level is 1-mover. I either couldn't find the right solution or the difficulty ot the game isn't progressing right. Controls felt a bit cluncky. Clicking the arrows is quite tedious. Maybe adding some kind of button controls (4 for choosing a side 3 for choosing which part of a cube you want to move) would be good addition. That or some kind of a swipe detection.
This game lacks mechanics. That need testing ofcourse, but since this is a platformer, some usual platformer mechanics like jumping platforms or spikes could add to a depth. Right now, the game gets boring as soon as you finish 1 hard level. You need to have some kind of progression during playthrough to keep people engaged. I would definitely recommend you make it more obvious which blocks are traversable and which aren't. Maybe adding some kind of an edge to them.
Music is good but gets annoying pretty fast, so few more musical compositions would be nice. Voicelines sound rather unprofessional. Its ok for the jam but I'm already thinking of this game as a full realease, so I'm a bit too crititcal here.
Overall, this is really cool idea for a hypercasual game. Good job