Not Newton's Sum

Algebra Level 4

Consider the cubic equation 245x3287x2+99x9=0 245x^3 - 287x^2 + 99x - 9 = 0 with roots α,β,γ \alpha , \beta , \gamma . If

r=0(αr+βr+γr) \displaystyle\sum_{r=0}^{\infty} \left ( \alpha^{r} + \beta^{r} + \gamma^{r} \right )

is of the form mn \frac {m}{n} , where mm and nn are coprime positive integers, what is value of mn+1? \frac {m}{n+1}?

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