Crazy Prime Equation

\[\large\dfrac{p}{{p + 1}} + \dfrac{{q + 1}}{q} = \dfrac{{2n}}{{n + 2}}\]

Let \(p,q\) and \(n\) be positive integers satisfying the equation above, with \(p \) and \(q\) are prime numbers. Find the sum of all possible values of \(q-p\).

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