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Algebra Level 4

\[\begin{align} \begin{cases} (x+2)(y+2) = 3(x^{2}+y^{2}+\sqrt{xy}) \\ (\sqrt{x}+\sqrt{y})^{3} = 4(x^{3}+ y^{3}) \end{cases} \end{align}\]

Given that positive reals \(x,y\) satisfy both equations. Determine the value of \(\sqrt{x}+\sqrt{y}\).

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