Only two, not three

Algebra Level 4

\[ \large \begin{cases} {x^3+5x^2+px+q=0} \\ {x^3+x^2+px+r=0 } \end{cases} \]

For variables \(p,q\) independent of \(x\), if the two equations above share exactly two common roots, find the sum of the two uncommon roots.

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