This paper studies how to maximize the per-user-based throughput in an M-tier heterogeneous wireless network (HetNet) by optimally managing traffic flows between the access points (APs) in the HetNet. The APs in the first M-1 tiers can use the licensed spectrum at the same time whereas they share the unlicensed spectrum with the APs in the Mth tier by the proposed opportunistic carrier sense multiple access with collision avoidance (CSMA/CA) protocol. The APs that access the licensed and unlicensed spectra simultaneously are able to integrate their spectrum resources by the carrier aggregation technique. We first characterize the distribution of the cell load and the channel access probability of each AP using a generalized AP association scheme. For an AP in each tier, the tight lower bounds on its mean spectrum efficiencies in the licensed and unlicensed spectra are derived for the general random models of the channel gain and AP association weights. We define the per-user link throughput and per-user network throughput based on the derived the mean spectrum efficiencies and maximize them by proposing the decentralized and centralized traffic management schemes for the APs in the first M-1 tiers under the constraint that the per-user link throughput of the tier-M APs must be above some minimum required value. Finally, a numerical example of coexisting LTE and WiFi networks is provided to validate our derived results and findings.