If \( \alpha x + \beta y = 109 \) is the equation of the chord of the ellipse \( \frac{x^2}{\alpha} + \frac{y^2}{\beta} = 1 \), whose mid point is \( \left( \frac{1}{2}, \frac{1}{4} \right) \), then \( \alpha + \beta \) is equal to