\[ \begin{eqnarray}
x^3 + y^2 + x^2 y + xy & = & 91 \\
x^4 + 2x^2 y + y^2 &= & 169 \\
\end{eqnarray} \]

If positive integers \(x,y\) satisfy the system of equations above, what is the value of \(x+y\)?

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