Mobile Edge Computing (MEC) is a key technology towards delay-sensitive and computation-intensive applications in future cellular networks. In this paper, we consider a multi-user, multi-server system where the cellular base station is assisted by a UAV, both of which provide additional MEC services to the terrestrial users. Via dual connectivity (DC), each user can simultaneously offload tasks to the macro base station and the UAV-mounted MEC server for parallel computing, while also processing some tasks locally. We aim to propose an online resource management framework that minimizes the average power consumption of the whole system, considering long-term constraints on queue stability and computational delay of the queueing system. Due to the coexistence of two servers, the problem is highly complex and formulated as a multi-stage mixed integer non-linear programming (MINLP) problem. To solve the MINLP with reduced computational complexity, we first adopt Lyapunov optimization to transform the original multi-stage problem into deterministic problems that are manageable in each time slot. Afterward, the transformed problem is solved using an integrated learning-optimization approach, where model-free Deep Reinforcement Learning (DRL) is combined with modelbased optimization. Via extensive simulation and theoretical analyses, we show that the proposed framework is guaranteed to converge and can produce nearly the same performance as the optimal solution obtained via an exhaustive search.