With the explosive growth of network traffic and the diversification of service demands, network slicing (NS) and dual connectivity (DC) are considered as promising technologies in wireless networks. In this paper, we propose a novel algorithm that solves the resource allocation problem of NS in heterogeneous networks with the assistance of DC, while satisfying the characteristic requirements of eMBB and URLLC services. Firstly, we model the scenario and formulate the optimization problem, which is proved as an NP-Hard problem. Secondly, due to the nonconvex and combinatorial nature, the dueling double deep Q-network with long short-term memory (LSTM-D3QN) is proposed to solve this problem, aiming to improve the overall network utility, while ensuring the quality of experience (QoE). Then, we analyze the complexity of the algorithm. Finally, the simulation results show that the proposed algorithm can maximize the total utility of the system, while guaranteeing the user QoE. Compared with LSTM-A2C and DQN, the proposed algorithm improves the long-term network utility by 2.6% and 7.2%, respectively. In addition, compared with the algorithm without DC under the conditions of no priority, eMBB priority and URLLC priority, the proposed algorithm improves the network utility by 4.2%, 2.1% and 4.1%, respectively.