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