Is Brute Force the only way?

Algebra Level 3

\[\large\dfrac{1}{20} + \dfrac{1}{30} + \dfrac{1}{42} + \dfrac{1}{56} + \dfrac{1}{72} + \dfrac{1}{90} = \dfrac{p}{q}\]

If \(p\) and \(q\) are coprime positive integers satisfying the above equation, find the value of \(p+q\).

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