Wow, Feliks - that's amazing!
I just got my coolest ever 6x6x6 BLD: 45:08.54 (14:26). Not that fast, but cool. I had finished all corners and all centers and was doing inner wings, and the cube exploded. I was 6 moves into the commutator, but since I count, I knew that. A few of the centers fell out (and several internal pieces came out!!!), but all of the center pieces were on the front face, and since I knew they were all solved, I knew they were all the same color. So I carefully started disassembling. A couple of the internal pieces fell on the floor, as well as a couple of those center pieces from that side, but again, that wasn't a problem for me. So I carefully took all the pieces apart I needed to in order to safely put it back together, placing them in places where I could find them, hunted around on the floor and found the extra pieces (which took a while - one of them went behind the chair - I'm sure it would have been very funny to watch as I was groping on the floor), and put it back together. Since I knew where all of the wings were, and I put the other side's centers in a safe place away from the first side's centers, I never had any doubt that I was putting it back together correctly. So I finished it, did the last two moves of my commutator (then redid the commutator to make sure I did the last two moves right, then undid it), and then finished the solve. And it was solved!
So awesome!