I Know the Pieces Fit

Algebra Level 5

Let \(x\) and \(y\) be real numbers such that
\( \begin{array} {l l }x^5+x^3y^2+x^2y^3+y^5 & =90240 \\ x^3+x^2+y^2+y^3 & =1036 \end{array} \)

What is the maximum integer value for \(x+y\)?

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