Let \( f:\mathbb{R}\to \mathbb{R} \) be a twice differentiable function such that the quadratic equation \( f(x)m^{2}-2f'(x)m+f''(x)=0 \) in \( m \) has two equal roots for every \( x\in\mathbb{R} \). If \( f(0)=1 \), \( f'(0)=2 \), and \( (\alpha,\beta] \) is the largest interval in which the function \( f\left(\log_{e}x - x\right) \) is increasing, then \( \alpha+\beta \) is equal to ________.
