This is the last problem of Newton's Sums I'll post

Algebra Level 4

Given that \(x\), \(y\) and \(z\) are complex numbers such that:

\(x+y+z=3\)

\(x^3+y^3+z^3=15\)

\(x^4+y^4+z^4=35\)

Find the sum of all the possible values of \(x^2(x^3+1)+y^2(y^3+1)+z^2(z^3+1)\).

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