Switching Balls

Consider two boxes each containing 10 identical red balls and 10 identical white balls. If one ball is drawn from the first and then replaced by one ball from the other, and then another ball is drawn from the first, what is the probability that at least one of the balls drawn from the first box is red? The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.