Cubes and Sixths

Algebra Level 5

Let the complex numbers \(a\), \(b\) and \(c\) be the roots of the equation \(x^3+3x+5=0\). Find the value of \[\frac{a^6-1}{a-1}+\frac{b^6-1}{b-1}+\frac{c^6-1}{c-1}.\]

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