Network slicing is a promising technique for wireless service providers to support enhanced mobile broadband (eMBB) and ultra-reliable low-latency communication (URLLC) services in a shared radio access network (RAN) infrastructure. In this paper, we apply numerology, mini-slot based transmission, and punctured scheduling techniques to support eMBB and URLLC network slices. For efficient allocation of radio resources (e.g., physical resource blocks, transmit power) to the users, we formulate RAN slicing problem as a multi-timescale problem. To solve this problem and address the dynamics of the traffic, we propose a hierarchical deep learning framework. Specifically, in each long time slot, the service provider employs a deep reinforcement learning (DRL) algorithm to determine the slice configuration parameters. The eMBB and URLLC schedulers use their own attention-based deep neural network (DNN) algorithm to allocate radio resources to their corresponding users in each short and mini time slot, respectively. Simulation results show that the proposed framework can achieve a higher aggregate throughput and a higher service level agreement (SLA) satisfaction ratio compared to some other RAN slicing approaches, including the resource proportional placement algorithm, decomposition and relaxation based resource allocation algorithm, and distributed bandwidth optimization algorithm.