A number theory problem by Akshat Sharda

Let \(a=\dfrac{(n+3)^3}{n-1}\) where \(a\) and \(n\) are integers.

Let the integral values of \(n\) satisfying the above equation be \(n_{1},n_{2},n_{3}, \ldots, n_{m}\).

Find \(\left(\displaystyle \sum^{m}_{p=1}n_{p}\right)+m\).

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