Fifth-Generation (5G) and sixth-Generation (6G) are new global wireless standards providing everyone and everything, machines, objects, and devices, with massive network capacity. The technological advances in wireless communication enable 5G and 6G networks to support resource and computation-hungry services such as smart agriculture and smart city applications. Among these advances are two state-of-the-art technologies: Carrier Aggregation (CA) and Multi Access Edge Computing (MEC). CA unlocks new sources of spectrum in both the mid-band and high-band radio frequencies. It provides the unique capability of aggregating several frequency bands for higher peak rates, and increases cell coverage. The latter is obtained by activating the Component Carriers (CC) in low-band and mid-band frequency (below 7 GHz) while 5G high-band (above 24GHz) delivers unprecedented peak rates with poorer Uplink (UL) coverage. MEC provides computing and storage resources with sufficient connectivity close to end users. These execution resources are typically within/at the boundary of access networks providing support for application use cases such as Augmented Reality (AR)/Virtual Reality (VR). The key technology in MEC is task offloading, which enables a user to offload a resource-hungry application to the MEC hosts to reduce the cost (in terms of energy and latency) of processing the application. This thesis focuses on using CA and task offloading in 5G and 6G wireless networks. These advanced infrastructures are an enabler for many broader use cases, e.g., autonomous driving and Internet of Things (IoT) applications. However, the pertinent problems are the high dimensional ones with combinatorial characteristics. Furthermore, the time-varying features of the 5G/6G wireless networks, such as the stochastic nature of the wireless channel, should be concurrently met. The above challenges can be tackled by using data-driven techniques and Machine Learning (ML) algorithms to derive intelligent and autonomous resource management techniques in the 5G/6G wireless networks. The resource management problems in these networks are sequential decision-making problems, additionally with conflicting objectives. Therefore, among the ML algorithms, the ones based on the Reinforcement Learning (RL), constitute a promising tool to make a trade-off between the conflicting objectives of the resource management problems in the 5G/6G wireless networks, are used. This research considers the objective of maximizing the achievable rate and minimizing the users’ transmit power levels in the MEC-enabled network. Additionally, we try to simultaneously maximize the network capacity and improve the network coverage by activating/deactivating the CCs. Compared with the derived schemes in the literature, our contributions are two folded: deriving distributed resource management schemes in 5G/6G wireless networks to efficiently manage the limited spectrum resources and meet the diverse requirements of some resource-hungry applications, and developing intelligent and energy-aware algorithms to improve the performance in terms of energy consumption, delay, and achievable rate.