\[\sum _{ n=0 }^{ \infty }{ \dfrac { 240 }{ (4n+5)(4n+6)(4n+7)(4n+9)(4n+10)(4n+11) } } =\dfrac { a }{ b } -c\pi \]

The equation above holds true for positive integers \(a,b\) and \(c\), with \(a,b\) coprime. Find \(a+b+c\).

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