We have a directrix and we have a focal point. What's missing?

Algebra Level 5

There is a parabola with directrix defined by the line

$3x + 7y = 21$

and focal point

$P = (3, 3).$

The equation of the parabola can be written as

$ax^2 + bxy + cy^2 + dx + ey + f = 0,$

where the $$\gcd\big(|a|, |b|, |c|, |d|, |e|, |f|\big) = 1$$. Find the maximum value of

$a + b + c + d + e + f.$

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