The interplay between symmetries and entanglement in out-of-equilibrium quantum systems is currently at the center of an intense multidisciplinary research effort. Here we introduce a setting where these questions can be characterized exactly by considering dual-unitary circuits with an arbitrary number of U(1) charges. After providing a complete characterization of these systems we show that one can introduce a class of solvable states, which extends that of generic dual-unitary circuits, for which the nonequilibrium dynamics can be solved exactly. In contrast to the known class of solvable states, which relax to the infinite-temperature state, these states relax to a family of nontrivial generalized Gibbs ensembles. The relaxation process of these states can be simply described by a linear growth of the entanglement entropy followed by saturation to a nonmaximal value but with maximal entanglement velocity. We then move on to consider the dynamics from nonsolvable states, combining the exact results with the entanglement membrane picture we argue that the entanglement dynamics from these states is qualitatively different from that of the solvable ones. It shows two different growth regimes characterized by two distinct slopes, both corresponding to submaximal entanglement velocities. Moreover, we show that nonsolvable initial states can give rise to the quantum Mpemba effect, where less symmetric initial states restore the symmetry faster than more symmetric ones.
