If the average length of all the vertical chords of the hyperbola

\(\displaystyle \dfrac{x^2}{9} - \dfrac{y^2}{4} = 1 \)

over the interval \(x \in (3,6) \) is

\(\large \displaystyle a[b \sqrt{c} - \ln(b + \sqrt{c})] \),

find \(a+b+c\)

**Details**

- \(c\) is square free.

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