Let the function \( f(x) = 2x^2 - \log_e x, \, x > 0 \), be decreasing in \( (0, a) \) and increasing in \( (a, 4) \). A tangent to the parabola \( y^2 = 4ax \) at a point \( P \) on it passes through the point \( (8a, 8a - 1) \) but does not pass through the point \( \left(-\dfrac{1}{a}, 0\right) \). If the equation of the normal at \( P \) is \( \dfrac{x}{\alpha} + \dfrac{y}{\beta} = 1 \), then \( \alpha + \beta \) is equal to ______.
