I have been able to level up half my elemental dragons past level 10. I don't know how to level my epic dragons past level 10, though.
You can't at this point, to level past 10 it has to be elemental.
If that were to change, and use the current system of shrines, you will be able to find details here:
If you participated in, and perfected, the Star Fall event, you received a special reward building that raises the level limit on Epic dragons to level 15. It did not effect Gemstone dragons, so their limit remains level 10 regardless.
Prior to this reward building, there was no way to raise the level limit of Epic dragons from the max level of 10.