Sum of Reciprocals from a Radical System

If $ x + y = \sqrt{5x - 4} + \sqrt{5y - 4} = 4 $, what is the sum of the reciprocals of $ x $ and $ y $? The answer is in the form $\frac{\alpha}{\beta}$ where $\alpha$ and $\beta$ are coprime positive integers. Input the value of $\alpha + \beta$.