  We mainly investigate a coupled system of the generalized nonlinear
Schr\"odinger equation and the Maxwell-Bloch equations which describes the wave
propagation in an erbium-doped nonlinear fiber with higher-order effects
including the forth-order dispersion and quintic non-Kerr nonlinearity. We
derive the one-fold Darbox transformation of this system and construct the
determinant representation of the $n$-fold Darboux transformation. Then the
determinant representation of the $n$th new solutions $(E^{[n]},\, p^{[n]},\,
\eta^{[n]})$ which were generated from the known seed solutions $(E, \, p, \,
\eta)$ is established through the $n$-fold Darboux transformation. The
solutions $(E^{[n]},\, p^{[n]},\, \eta^{[n]})$ provide the bright and dark
breather solutions of this system. Furthermore, we construct the determinant
representation of the $n$th-order bright and dark rogue waves by Taylor
expansions and also discuss the hybrid solutions which are the nonlinear
superposition of the rogue wave and breather solutions.
