\[\large \int_ {-\infty}^{\infty}{\frac{\cos{(3x)}}{ {({x}^{2}+25)}^{2} }} \, dx \]

If the value of the above integral is equals to \(\large \frac{a\pi}{b {e}^{c}} \) where \(e\) is Euler's number and \(a,b\) are coprime positive integers, what is the value of \(a+b+c\)?

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