My first ever problem

Algebra Level pending

Consider a polynomial \(P(x)\) such that \(P(x)=\displaystyle \sum _{ n=1 }^{ 7 }{ \phi (n)x^{ n } }\) and \(x_{ 1 },x_{ 2 },x_{ 3 }, ...,x_{ 7 }\) are the roots of \(P(x)=0\).

Find \( \displaystyle \sum _{ n=1 }^{ 7 }{ x_{ n }^{ 3 }}\).

The answer is in the form \( -\frac { p }{ q }\), where \(p\) and \(q\) are co-prime positive integers, find \(p+q\).

Note: \(\phi (n)\) denotes Euler's totient function.

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