If the coefficient of \(x^{15}\) in the expansion of \(\left(a x^3+\frac{1}{b x^{\frac{1}{3}}}\right)^{15}\) is equal to…

If the coefficient of \(x^{15}\) in the expansion of \(\left(a x^3+\frac{1}{b x^{\frac{1}{3}}}\right)^{15}\) is equal to the coefficient of \(x^{-15}\) in the expansion of \(\left(a x^{\frac{1}{3}}-\frac{1}{b x^3}\right)^{15}\), where \(a\) and \(b\) are positive real numbers, then for each such ordered pair \((a, b)\) :

[JEE Main 2023, 30 Jan (Shift 1)]