Many applications such as autonomous swarming drones and system services like data replication need to exchange data among many or all nodes in a network. However, wireless many-to-many broadcast has thus far only been studied theoretically or in simulation, and practical solutions hardly meet the requirements of emerging applications, especially in terms of latency. This paper presents Mixer, a communication primitive that provides fast and reliable many-to-many broadcast in dynamic wireless multi-hop networks. Mixer integrates random linear network coding with synchronous transmissions to simultaneously disseminate all messages in the network. To deliver the performance gains our approach enables, we design Mixer's protocol logic in response to the physical-layer characteristics and the theory of network coding. First results from testbed experiments demonstrate that, compared with the state of the art, Mixer is up to 65% faster and reduces radio-on time by up to 50%, while providing a message delivery rate above 99.9%.