We present a framework for visual action planning of complex manipulation tasks with high-dimensional state spaces, focusing on manipulation of deformable objects. We propose a Latent Space Roadmap (LSR) for task planning, a graph-based structure capturing globally the system dynamics in a low-dimensional latent space. Our framework consists of three parts: (1) a Mapping Module (MM) that maps observations, given in the form of images, into a structured latent space extracting the respective states, that generates observations from the latent states, (2) the LSR which builds and connects clusters containing similar states in order to find the latent plans between start and goal states extracted by MM, and (3) the Action Proposal Module that complements the latent plan found by the LSR with the corresponding actions. We present a thorough investigation of our framework on two simulated box stacking tasks and a folding task executed on a real robot.