Inspired by a NT problem from BMO

If $n$ is a positive integer greater than 6 and 720 divides $n^2 (n^2+16)$ then sum of all possible remainders (not necessarily distinct) obtained on dividing $n+1$ and $n-1$ by 2, 3, 5 will be equal to $\text{\_\_\_\_\_\_\_\_\_\_\_}$ .