I am thinking of a number.

If I add 11 to my number, I get a perfect square*.

If I subtract 78 from my number, I also get a perfect square.

What is my number?

* A perfect square is a number which can be written as the square of an integer. For example 144 is a perfect square as 144 = 12². Similarly, 361 is a perfect square as 361 = 19².