Not Newton's Sum

Algebra Level 4

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

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

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

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