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