Let \( \cos(\alpha + \beta) = -\dfrac{1}{10} \) and \( \sin(\alpha - \beta) = \dfrac{3}{8} \), where \( 0<\alpha<\dfrac{\pi}{3} \) and \( 0<\beta<\dfrac{\pi}{4} \).
If
\[
\tan 2\alpha = \frac{3(1 - r\sqrt{5})}{\sqrt{11}(s + \sqrt{5})}, \quad r, s \in \mathbb{N},
\]
then the value of \( r + s \) is ______________.