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Algebra Level 5

\[ \begin{cases} a+b+c= 0 \\ a^5 + b^5 + c^5 = 5 \\ a^6 + b^6 + c^6 = 6 \end{cases} \]

Let \(a,b\) and \(c\) be numbers satisfying the system of equations above. And at least one of \(a,b\) and \(c\) is not a real number.

Given that \(a^2+b^2+c^2\) satisfy a least degree monic polynomial \(f(X) \), find \(f(2) \).

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