Binomial Theorem

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