Slippery Sum!

Calculus Level 4

\[ \displaystyle\sum _{ r=1 }^{ \infty }{ \frac { r\left( r+1 \right) }{ { 3 }^{ r } } } \]

If the summation above equals to \( \frac m n \) for coprime positive integers \(m,n\), what is the value of \(m+n\)?

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