Roots Relation

Algebra Level 5

24x415x3+1 \large 24x^4 - 15x^3 + 1

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

Image Credit: Wikimedia William Anthony Granville.
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