To solve equations

Algebra Level 3

\[\begin{cases}(\frac{x}{y})^{5}+5(\frac{x}{y}) =y^{5}+5y \\ x^{2016} +y^{4032} =2 \end{cases}\]

There are two solutions \((x_1, y_1)\) and \((x_2, y_2)\) to the equations above. What is \(x_1 + x_2 + y_1 + y_2?\)

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