Real numbers r and s are roots of p(x)=x^{3}+a x+b, and r+4 and s-3 are roots of q(x)=x^{3}+a x+b+240. Find the sum of all possible values of |b|.
Real numbers r and s are roots of p(x)=x^{3}+a x+b, and r+4 and s-3 are roots of q(x)=x^{3}+a x+b+240. Find the sum of all possible values of |b|.