$S =\frac{1}{5} + \frac{1}{5^{2}} + \frac{2}{5^{3}} + \frac{3}{5^{4}} + \frac{5}{5^{5}} + \frac{8}{5^{6}} + \cdots$

If $S = \dfrac AB$, where $A$ and $B$ are coprime positive integers, find the value of $A+B$.

**Clarification**: $1,1,2,3,5,8,\ldots$ follows the Fibonacci Sequence.

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