The sixth-generation (6G) communication networks are anticipated to enable a variety of innovative applications and provide extreme connectivity for mobile devices. To meet the evolving service demands in highly dynamic network environments, mobile edge computing (MEC) and artificial intelligence (AI) will be two pivotal technologies in 6G. MEC extends computing and storage capabilities within radio access networks, coping with the increasing computing demands from mobile users. Meanwhile, AI facilitates intelligent resource management by enabling network entities to learn and build knowledge about network dynamics. In this talk, we will explore AI-assisted resource management for MEC-enabled networks, addressing the computing challenges caused by device mobility and heterogeneity. We will introduce two AI-assisted resource management approaches, each tailored to support a representative MEC use case: the Internet of Vehicles and mobile virtual reality video streaming. Finally, we will outline a future research plan focused on holistic network virtualization through digital twin technologies, aimed at further enhancing the flexibility and efficiency of AI-assisted network management towards 6G.