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Dexterous manipulation of unknown objects performed by robots equipped with mechanical hands represents a critical challenge. The difficulties arise from the absence of a precise model of the manipulated objects, unpredictable environments, and limited sensing capabilities of the mechanical hands compared to human hands. This paper introduces a data-driven approach that provides a learning-based planner for dexterous manipulation employing an Adaptive Neuro-Fuzzy Inference System (ANFIS) fed by data obtained from an analytical manipulation planner. ANFIS captures the complex relationships between inputs and optimal manipulation parameters. Moreover, during a training phase, it is able to fine-tune itself on the basis of its experiences. The proposed planner enables a robot to interact with objects of various shapes, sizes, and material properties while providing an adaptive solution for increasing robotic dexterity. The planner is validated in a real-world environment, applying an Allegro anthropomorphic robotic hand. A link to a video of the experiment is provided in the paper.