A equation involving prime.

Find sum of all positive integers \(m\),\(n\) and primes \(p≥5\) such that

\(m(4m^{2}+m+12)=3(p^{n}-1)\).

For example, if the solutions are \((1,2,5)\) and \((3,2,7)\) then the answer will be

\(1+2+5+3+2+7=20\)

This is a INMO problem.

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