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Let $r_1,r_2,r_3,r_4$ be roots of the polynomial $x^4-4x^3+6x^2+8x+10$.

$\dfrac{1}{r_2+r_3+r_4}+\dfrac{1}{r_1+r_3+r_4}+\dfrac{1}{r_1+r_2+r_4}+\dfrac{1}{r_1+r_2+r_3}=\dfrac{A}{B}$

where $A$ and $B$ are co-prime positive integers. Find $A+B$.

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