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Legged robots have shown remarkable advantages in navigating uneven terrain. However, realizing effective locomotion and manipulation tasks on quadruped robots is still challenging. In addition, object and terrain parameters are generally unknown to the robot in these problems. Therefore, this paper proposes a hierarchical adaptive control framework that enables legged robots to perform loco-manipulation tasks without any given assumption on the object's mass, the friction coefficient, or the slope of the terrain. In our approach, we first present an adaptive manipulation control to regulate the contact force to manipulate an unknown object on unknown terrain. We then introduce a unified model predictive control (MPC) for loco-manipulation that takes into account the manipulation force in our robot dynamics. The proposed MPC framework thus can effectively regulate the interaction force between the robot and the object while keeping the robot balance. Experimental validation of our proposed approach is successfully conducted on a Unitree A1 robot, allowing it to manipulate an unknown time-varying load up to $7$ $kg$ ($60\%$ of the robot's weight). Moreover, our framework enables fast adaptation to unknown slopes (up to $20^\circ$) or different surfaces with different friction coefficients.