Maths and Palindromes

See if you can work this out...

I have two mystery numbers. For the purpose of this we'll call them X and Y. Both numbers are different, and both look completely random, and yet when you add them together you get a palindrome (a number that can be reversed and still be the same like 11 or 282). These two numbers also can be squared and added to each other and still be a palindrome, and even cubed and added together.

Your mission (should you choose to accept it) is simple, what is X, and what is Y?