Binomial Theorem and Its Simple Applications - Hard

If the coefficient of

x^{15}

in the expansion of

(ax^3 + \frac{1}{bx^{1/3}})^{15}

is equal to the coefficient of

x^{15}

in the expansion of

(ax - \frac{1}{bx^2})^{15}

, where

a

and

b

are positive real numbers, then for each such ordered pair

(a, b)