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 $(\mathrm{a}, \mathrm{b})$ :