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Algebra Level 5

Find the sum of all complex values of the parameter \(A\), such that that polynomial \[\begin{align} f_A(x)=& x^6+6x^5+5x^4-30x^3-74x^2-72x \\ & +A\left(x^4+5x^3+9x^2+8x\right) \\ \end{align} \]

can be expressed as \( g(h(x) ) \), where \(g(x) \) and \(h(x) \) are non-linear polynomials with complex coefficients.

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