Let \((a_1,b_1),(a_2,b_2),\dots, (a_n,b_n),\) be the ordered pairs \((a,b)\) of real numbers such that the polynomial \(p(x) = (x^2 + ax + b)^2 +a(x^2 + ax + b) - b\) has exactly one real root and no nonreal complex roots. Find \(a_1 + b_1 + a_2 + b_2 + \dots + a_n + b_n.\)
