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

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)]