Mathematics Question from JEE Main 2026 · 22 January, Shift 2

Let $L$ be the line $\frac{x+1}{2} = \frac{y+1}{3} = \frac{z+3}{6}$ and let $S$ be the set of all points $(a,b,c)$ on $L$, whose distance from the line $\frac{x+1}{2} = \frac{y+1}{3} = \frac{z-9}{0}$ along the line $L$ is $7$. Then $\sum_{(a,b,c)\in S} (a+b+c)$ is equal to