Divisible by 6

Let p,qp,q be two prime numbers such that 6pq+(p+1)(q+1)(p+q)6\mid pq+(p+1)(q+1)(p+q)

If (p,q)=(p1,q1),(p2,q2),,(pn,qn)(p,q)=(p_1,q_1),(p_2,q_2),\ldots, (p_n,q_n) are all solutions for the ordered pair (p,q)(p,q) then find i=1npi+qi.\sum_{i=1}^np_i+q_i.

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