Can you spot the trick?

Calculus Level 4

\[\large\mathfrak R=\displaystyle\sum_{x=1}^{\infty}\dfrac{x^5-9x}{x^8-3x^6+27x^2-81}\]

If \(\mathfrak R\) can be written in the form \(\dfrac pq\), where \(p\) and \(q\) are coprime positive integers, find \(|p-q|\).

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