Can you find the ordered pairs?

Algebra Level 3

{2x2+y+2x+y2=128x+y=8\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,yx,y that satisfy the system of equations above.

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