\[ \large 24x^4 - 15x^3 + 1 \]
###### Image Credit: Wikimedia William Anthony Granville.

Let \(a,b,c,d\) be the roots of the polynomial above. If \((abc)^3+(abd)^3+(acd)^3+(bcd)^3 = \frac pq\) for coprime positive integers \(p,q\), find the value of \(p+q\).

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