What a messy problem

Algebra Level pending

The right side of this equation: \(8=\sqrt{x^{3}-3x^{2}+3x-1}\) can be rewritten as: \((x-a)^{\frac{b}{c}}\). Then, \(\frac{2x+c}{3b-a}\) can be written as \(\frac{m}{n}\), where \(m\) and \(n\) are positive coprime integers. Find \(m+n\).

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