We study the resource allocation problem in RAN-level integrated HetNets. This emerging HetNets paradigm allows for dynamic traffic splitting across radio access technologies for each client, and then for aggregating the traffic inside the network to improve the overall resource utilization. We focus on the max-min fair service rate allocation across the clients, and study the properties of the optimal solution. Based on the analysis, we design a low complexity distributed algorithm that tries to achieve max-min fairness. We also design a hybrid network architecture that leverages opportunistic centralized network supervision to augment the distributed solution. We analyze the performance of our proposed algorithms and prove their convergence. We also derive conditions under which the outcome is optimal. When the conditions are not satisfied, we provide constant upper and lower bounds on the optimality gap. Finally, we study the convergence time of our distributed solution and show that leveraging appropriate policies in its design significantly reduces the convergence time.