The goal of algorithmic recourse is to reverse unfavorable decisions under automated decision making by suggesting actionable changes (e.g., reduce the number of credit cards). Such changes allow individuals to achieve favorable outcomes (e.g., loan approval) under low costs for the affected individual. To suggest low cost recourse, several recourse methods have been proposed in recent literature. These techniques usually generate recourses under the assumption that the features are independently manipulable. This, however, can be misleading since the omission of feature dependencies comes with the risk that some required recourse changes are overlooked. In this work, we propose a novel, theory-driven framework, DisEntangling Algorithmic Recourse (DEAR), that suggests a solution to this problem by leveraging disentangled representations to find interpretable, small-cost recourse actions under input dependencies. Our framework addresses the independently manipulable feature (IMF) assumption by dissecting recourse actions into direct and indirect actionable changes.