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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