Progress: 76.45% (2922 / 3822)
Let \(a\) and \(b\) be positive integers satisfying \(\frac{ab+1}{a+b}<\frac{3}{2}\). The maximum possible value of \(\frac{a^3b^3+1}{a^3+b^3}\) is \(\frac{p}{q}\), where \(p\) and \(q\) are relatively prime positive integers. Find \(p+q\).