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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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