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Humanoid loco-manipulation is often simplified into a stop-and-go process: walking to an object, stopping to manipulate it, and then resuming locomotion. It also commonly relies on low degree-of-freedom (DoF) end effectors that behave like an open-close grasp primitive. We introduce CoorDex, a learning pipeline that converts high-dimensional body and dexterous hand control into coordinated latent residual control, enabling high-DoF dexterous loco-manipulation on the move. Starting from simulated whole-body and hand demonstrations, CoorDex trains privileged motion tracking teachers for the humanoid body and dexterous hand, distills them into proprioception-conditioned latent priors, and uses the frozen priors as the action space for downstream residual reinforcement learning. A coordinated latent residual policy composes these priors through shared task context and separate body-hand residual heads, preserving natural whole-body motion while improving finger-level contact reliability. CoorDex enables a Unitree G1 humanoid with a 20-DoF WUJI hand to execute dexterous manipulation while in motion, including non-stop bottle grasping and carrying, fridge door opening on the move, and cube pick-and-turn. Ablations on the walk-grasp-carry task show that joint-space PPO, joint-space hand control, and monolithic latent prediction all fail under the same reward budget, while the latent-prior interface and coordinated residual structure make high-dimensional contact-rich loco-manipulation trainable. Project Page: this https URL