PolyAMO0109

Algebra Level 4

There is a unique pair of non-zero real numbers that satisfy the following system of equations

\[\large \begin{cases} (1+x)(1+ x^{2})(1+ x^{4})=1+ y^{7} \\ (1+y)(1+ y^{2})(1+ y^{4})=1+ x^{7} \end{cases} \]

Submit your answer as \(x+y\).

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