Exponential And Polynomials In One Sum?

Algebra Level 5

\[\large \displaystyle \sum_{n = 2}^{\infty} \dfrac{n^4 + 3n^2 + 10n + 10}{2^{n} (n^4 + 4)} = \dfrac ab \]

The above equation is true for some coprime positive integers \(a\) and \(b\). Find \(a + b\)?

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