We study the problem of decentralized task offloading and load-balancing in a dense network with numerous devices and a set of edge servers. Solving this problem optimally is complicated due to the unknown network information and random task sizes. The shared network resources also influence the users' decisions and resource distribution. Our solution combines the mean field multi-agent multi-armed bandit (MAB) game with a load-balancing technique that adjusts the servers' rewards to achieve a target population profile despite the distributed user decision-making. Numerical results demonstrate the efficacy of our approach and the convergence to the target load distribution.