Future cellular networks will be dense and require key traffic management technologies for fine-grained network control. The problem gets more complicated in the presence of different network segments with bottleneck links limiting the desired quality of service (QoS) delivery to the last mile user. In this work, we first design a framework for software-defined cellular networks (SDCN) and then propose new mechanisms for management of QoS and non-QoS users traffic considering both access and backhaul networks, jointly. The overall SDN-LTE system and related approaches are developed and tested using network simulator (ns-3) in different network environments. Especially, when the users are non-uniformly distributed, the results shows that compared to other approaches, the proposed load distribution algorithm enables at least 6\% and 23\% increase in the average QoS user downlink (DL) throughput for all network users and 40\%-ile edge users, respectively. Also, the proposed system efficiently achieves desired QoS and handles the network congestion without incurring significant overhead.