A discrete mathematics problem by Santiago Hincapie

\[\large{ \sum _{ n=1 }^{ \infty }{ \frac { F_{ n } }{ { x }^{ n } } =\frac { x }{ 505 } } }\]

Find the value of \(x, \ x > 0\) such that the above equation satisfies where \(F_n\) denotes the \(n^{\text{th}}\) Fibonacci number.

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