Get the value \(x+y\)

Number Theory Level 2

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

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

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