No problem, Double Integral!

Calculus Level 5

If \[\large \displaystyle \int_{0}^{\infty} \dfrac{\sin^3 x}{x^3} dx \ = \ A \] and \[\large \displaystyle \int_{0}^{\infty} \left (\dfrac{x - \sin x}{x^3} \right ) dx \ = \ \dfrac{m A}{n} \] where \(m\) and \(n\) are positive relative coprimes, then what is \(m+n \)?.

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