In this paper, we propose a novel load balancing routing algorithm for wireless mesh networks (WMNs) with multiple gateways, i.e., sink routers. As most traffic occurring in WMNs is relayed to these gateways through wireless links in a multi-hop fashion, the sink routers are easily overloaded. In such a situation, when a user initiates a communication session and the corresponding route toward the sink router cannot provide the required level of services, the session is rejected. Our objective is to achieve load balancing routing that minimizes such rejections. To this end, we take an adaptive partitioning approach, which heuristically divides the entire network into partitions and applies load balancing to between partitions and within partitions. To cope with user mobility, partitions and routes are adaptively managed. Evaluation via simulations indicates up to 25% performance gains over existing schemes in rejected requests, while the overhead in route computation costs drops by up to 27%.