$p, q, r$ are real numbers satisfying the following equations:  
\[ \frac{(p+q)(q+r)(r+p)}{pqr} = 24 \]  
\[ \frac{(p-2q)(q-2r)(r-2p)}{pqr} = 10. \]  
Given that \( \frac{p}{q} + \frac{q}{r} + \frac{r}{p} \) can be expressed in the form \( \frac{m}{n} \), where \( m, n \) are relatively prime positive integers, compute \( m+n \).

Let's think step by step and output the final answer within \boxed{}.
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