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With the emerging Internet of Things paradigm, massive Machine-Type Communication (mMTC) has been identified as one of the prominent services that enables a broad range of applications with various Quality of Service (QoS) requirements for 5G-and-beyond networks. However, it is very difficult to employ a monolithic physical network to support various mMTC applications with differentiated QoS requirements. Moreover, in ultra-dense mobile networks, the scarcity of the preamble and Physical Downlink Control CHannel (PDCCH) resources may easily lead to resource collisions when a large number of devices access the network simultaneously. To tackle these issues, in this paper, we propose a network slicing-enabled intelligent random access framework for mMTC. First, by tailoring a gigantic physical network into multiple lightweight network slices, fine-grained QoS provisioning can be accomplished, and the collision domain of Random Access (RA) can be effectively reduced. In addition, we propose a novel concept of sliced preambles (sPreambles), based on which the transitional RA procedure is optimized, and the issue of preamble shortage is effectively relieved. Furthermore, with the aim of alleviating PDCCH resource shortage and improving transmission efficiency, we propose a learning-based resource-sharing scheme that can intelligently multiplex the PDCCH resources in the naturally dynamic environment. Simulation results show that the proposed framework can efficiently allocate resources to individual mMTC devices while guaranteeing their QoS requirements in random access processes.