Gamma Funk'tion

Algebra Level 1

Evaluate \[\dfrac{\Gamma\left(\frac {16}{3}\right)}{\Gamma\left(\frac{10}{3}\right)},\] where \(\Gamma (z)\) denotes the gamma function.

If the value of the above expression can be expressed in the form of \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).