Oh no not cubics!

Algebra Level 4

Let \(a,\) \(b,\) and \(c\) be the roots of the cubic equation \(7x^3-14x^2+21x-28=0.\) If \(\dfrac{a}{bc} ,\) \(\dfrac{b}{ac},\) and \(\dfrac{c}{ab}\) are the roots of the equation \(x^3+rx^2+sx+t,\) the value of \(\dfrac{r}{s}\) can be expressed as \(-\dfrac{p}{q},\) where \(p\) and \(q\) are coprime positive integers. Find \(p+q.\)

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