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Wireless Mesh Networks (WMNs) are envisaged to extend Internet access and other networking services in personal, local, campus, and metropolitan areas. Mesh routers (MR) form the connectivity backbone while performing the dual tasks of packet forwarding as well as providing network access to the mesh clients. However, the performance of such networks is limited by traffic congestion, as only limited bandwidth is available for supporting the large number of nodes in close proximity. This problem can be alleviated by the cognitive radio paradigm that aims at devising spectrum sensing and management techniques, thereby allowing radios to intelligently locate and use frequencies other than those in the 2.4 GHz ISM band. These promising technologies are integrated in our proposed Cognitive Mesh NETwork (COMNET) algorithmic framework, thus realizing an intelligent frequency-shifting self-managed mesh network. The contribution of this paper is threefold: (1) A new approach for spectrum sensing is devised without any change to the working of existing de facto mesh protocols. (2) An analytical model is proposed that allows MRs to estimate the power in a given channel and location due to neighboring wireless LAN traffic, thus creating a virtual map in space and frequency domains. (3) These models are used to formulate the task of channel assignment within the mesh network as an optimization problem, which is solved in a decentralized manner. Our analytical models are validated through simulation study, and results reveal the benefits of load sharing by adopting unused frequencies for WMN traffic.