Modular Cubes, Part 1
For a positive number $n$, define $S(n)$ as the sum of the integers $x$, for which $1 \lt x \lt n$ and
$x^3 \equiv 1 \bmod n$.
When $n=91$, there are $8$ possible values for $x$, namely: $9, 16, 22, 29, 53, 74, 79, 81$.
Thus, $S(91)=9+16+22+29+53+74+79+81=363$.
Find $S(13082761331670030)$.