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This paper deals with the problem of load-balanced routing in multi-radio multi-rate multi-channel wireless mesh networks. Our analysis relies on the multicast and broadcast sessions, where each session has a specific bandwidth requirement. We show that using both rate and channel diversity significantly improves the network performance. Toward this goal, we propose two cross-layer algorithms named the ''Interference- and Rate-aware Multicast Tree (IRMT)'' and the ''Interference- and Rate-aware Broadcast Tree (IRBT)''. The proposed algorithms jointly address the problems of routing tree construction, transmission channel selection, transmission rate selection, and call admission control. As an advantage, the IRMT and the IRBT algorithms consider both inter-flow and intra-flow interference. These schemes not only improve the utilization of the network resources, but also balance the traffic load over the network. Numerical results demonstrate the efficiency of the proposed algorithms in terms of the number of transmissions, the load-balancing, and the network throughput.