Modern web services rely on a network of distributed cache servers to efficiently deliver content to users. Load imbalance among cache servers can substantially degrade content delivery performance. Due to the skewed and dynamic nature of real-world workloads, cache servers that serve viral content experience higher load as compared to other cache servers. We propose a novel distributed load balancing protocol called Meezan to address the load imbalance among cache servers. Meezan replicates popular objects to mitigate skewness and adjusts hash space boundaries in response to load dynamics in a novel way. Our theoretical analysis shows that Meezan achieves near perfect load balancing for a wide range of operating parameters. Our trace driven simulations shows that Meezan reduces load imbalance by up to 52% as compared to prior solutions.