Cellular traffic prediction at mobile edges is extremely valuable to ultra high-reliability low-latency (URLLC) communication of 5G. Many network actions depend on this prediction technology, ranging from radio resource scheduling, edge node sharing, and traffic control, to network slicing and dynamic network function virtualization. However, accurate prediction for cellular traffic flow is a tough challenge, since irregular and dramatic fluctuations of network traffic, caused by continuous topology update and multifarious service requests, occur frequently. Motivated by these investigations, we propose a deep multi-reservoir regression learning network for cellular traffic prediction, called mRDLN, supporting multi-access edge computing. This architecture is a uniform and consistent system with functional modules of smoothing, feature extraction, and multi-reservoir regression. This is the first attempt to enhance deep neural computing considering a combined regression scheme in the framework of a deep belief network, where multiple echo state networks are integrated to perform local supervised learning instead of the original single approximator. On highly bursty cellular traffic traces, experimental simulations show that our mRDLN consistently outperforms the state-of-the-art models, and the superior prediction is further verified by means of statistical analysis.