Rational Equation

If the numerator and denominator of a certain fraction are both increased by 5, the resulting fraction is $\frac{5}{21}$ larger than the original fraction. If the numerator and denominator of the same fraction are both decreased by 1 instead, the resulting fraction is $\frac{2}{21}$ lower than the original fraction. What is the original fraction in lowest terms? The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.