Can you find the ordered pairs?

Algebra Level 3

\[\large {\begin{cases}{2^{x^2+y} + 2^{x+y^2} = 128} \\ { \sqrt{x} + \sqrt{y} = \sqrt{8} } \end{cases} } \]

Find the sum of all real numbers \(x,y\) that satisfy the system of equations above.


This problem is inspired by a problem from the Regional Mathematics Olympiad 2011, India.
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