Vehicle-to-everything (V2X) communication enables connected autonomous vehicles (CAVs) to share information and generate optimal decisions. The networking abilities of CAVs have led to the development of unsignalized autonomous intersection management (AIM) methods that leverage CAVs to significantly improve traffic flows. However, AIM methods assume 100% CAV market penetration, which is currently unrealistic owing to the gradual adoption of CAVs. Therefore, CAVs must share road usage with nonconnected vehicles (NCVs). Thus, we propose a mixed-traffic intersection management method that considers NCVs while ensuring high traffic flow, called traffic-load-responsive reservation for intersection management (TLRRIM). In TLRRIM, the roadside unit (RSU) first classifies vehicles and groups them into clusters before selecting a reservation cluster to cross an intersection. The reservation cluster selection considers both traffic load and crossing urgency. In addition, the RSU utilizes V2X-enabled speed coordination (VESC) for CAVs within the reservation cluster to further improve traffic flow, while utilizing traffic lights to guide NCVs. Simulation-based experiments using OpenCDA and CARLA showed that TLRRIM can increase throughput and reduce waiting time by up to 89.63% and 60.71 %, respectively, compared with the fixed-time signaling method. Moreover, adding VESC can increase throughput by 12.21 % and reduce waiting time by 10.80%, further enhancing traffic flow.