There is only one answer when you take into account that certain numbers need to be opposite each other
The way I worked it out was by observing that the dice has landed each time on a different axis, If it had been the same axis at least 2 of the sides (total - front & top) would have been the same value. I then did a brute force by assuming first that the third throws top and front was 1,5 and then 2,4. This would mean that the sides for the first two throws would both need to include either 1 or 5, or 2 or 4. also means that we can eliminate (1,15 and 5,11) or (2,14 and 4,12) from the third throw. From there it is reasonably easy to prove that the third throw cannot be (1,5) on the top & face. (2,4) on the top & face. is a little more tricky and I would suggest drawing a cube with possible values on each respective face. In the end I found that only Writersblock's answer existed.
An interesting follow up question would be if Morty cheated by switching dice between 3 dice with the same numbers (2,4,5,7,8,11) but different configurations could he ensure that there would be no possible solution no matter which way the dice landed on each throw?
NOTE I haven't personally figured this out yet