Let the latus rectum of the hyperbola \( \dfrac{x^2}{9} - \dfrac{y^2}{b^2} = 1 \) subtend an angle of \( \dfrac{\pi}{3} \) at the centre of the hyperbola. If \( b^2 \) is equal to \( \dfrac{l}{m}(1 + \sqrt{n}) \), where \( l \) and \( m \) are co-prime numbers, then \( l^2 + m^2 + n^2 \) is equal to \( \_\_\_\_\_\_\_\_ \).
