database sharding or read replicas for scaling?

Hey everyone, I'm wrestling with scaling a read-heavy application and trying to decide between sharding our primary database or just adding more read replicas. We've hit a bottleneck on writes, but also see spikes in read traffic. What are your experiences with these approaches? When did you choose one over the other, and what were the trade-offs you encountered? I'm particularly interested in the operational overhead and complexity involved with each.