Sum Cool Squares.

There exists two 4-digit numbers \(\overline{abcd}\) such that \[\overline{ab} ^{2} + \overline{cd} ^{2} = \overline{abcd}.\] What is the sum of those two numbers?

Note:
\({a,b,c,d}\) are digits, not factors of a product.
\( a \neq 0 \).
Also, this problem is not original.

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