What is the equation of the plane which contains the following two parallel lines:
\[ \frac{x+1}{6} = \frac{y-2}{7} = z \hspace{.3cm} \text{ and } \hspace{.3cm} \frac{x-3}{6} = \frac{y+4}{7} = z-1?\]

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The equation of the plane that passes through the three points:
\[\begin{array}&(0,-2,3),&&(1,0,1),&&(-1,-1,0)\end{array}\]
is \(ax+by+cz+1=0.\) Find the value of \(a+b+c.\)

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