\[x^3-24x^2+180x-420=0\]

A \(\triangle ABC\) has sides \(a,b\) and \(c\). It is known that \(a,b\) and \(c\) are also the roots of the equation above.

Given that \(\cos A+\cos B+\cos C =\dfrac{p}{q}\), where \(p\) and \(q\) are coprime positive integers, find the value of \(11(p+q)+25\).

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