Mobile Edge Computing (MEC) is a key technology for the deployment of next generation (5G and beyond) mobile networks. The computational power it provides at the edge could allow providers to fulfill the requirements of use cases in need of ultra-low latency, high bandwidth, as well as real-time access to the radio network. However, this potential needs to be carefully administered as the edge is certainly limited in terms of computation capability, as opposed to the cloud which holds the promise of a virtually infinite power. MEC nodes, though, could still try to exploit not only their local capacity, but also the one that the neighbor MEC nodes could offer. Considering that the 5G scenario assumes an ultra-dense distribution of MEC nodes, this possibility could be feasible, provided that we find an effective way to carefully allocate the resources available at each edge node. In this paper, we provide an optimization framework that considers several key aspects of the resource allocation problem with cooperating MEC nodes. We carefully model and optimize the allocation of resources, including computation and storage capacity available in network nodes as well as link capacity. Specifically, our proposed model jointly optimizes (1) the user requests admission decision (2) their scheduling, also called calendaring (3) and routing as well as (4) the decision of which nodes will serve such user requests and (5) the amount of processing and storage capacity reserved on the chosen nodes. Both an exact optimization model and an effective heuristic, based on sequential fixing, are provided. Furthermore, we propose a distributed approach for our problem, based on the Alternating Direction Method of Multipliers (ADMM), so that resource allocation decisions can be made in a distributed fashion by edge nodes with limited overhead. We perform an extensive numerical analysis in several real-size network scenarios, using real positions for radio access points of a mobile operator in the Milan area. Results demonstrate that the heuristic performs close to the optimum in all considered network scenarios, while exhibiting a low computing time. This provides an evidence that our proposal is an effective framework for optimizing resource allocation in next-generation mobile networks.