Let a and b be positive integers satisfying \frac{a b+1}{a+b}<\frac{3}{2}. The maximum possible value of \frac{a^{3} b^{3}+1}{a^{3}+b^{3}} is \frac{p}{q}, where p and q are relatively prime positive integers. Find p+q.
Let a and b be positive integers satisfying \frac{a b+1}{a+b}<\frac{3}{2}. The maximum possible value of \frac{a^{3} b^{3}+1}{a^{3}+b^{3}} is \frac{p}{q}, where p and q are relatively prime positive integers. Find p+q.