Slippery Sum!

Calculus Level 4

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

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

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