Many query-based approaches for 3D Multi-Object Tracking (MOT) adopt the tracking-by-attention paradigm, utilizing track queries for identity-consistent detection and object queries for identity-agnostic track spawning. Tracking-by-attention, however, entangles detection and tracking queries in one embedding for both the detection and tracking task, which is sub-optimal. Other approaches resemble the tracking-by-detection paradigm, detecting objects using decoupled track and detection queries followed by a subsequent association. These methods, however, do not leverage synergies between the detection and association task. Combining the strengths of both paradigms, we introduce ADA-Track, a novel end-to-end framework for 3D MOT from multi-view cameras. We introduce a learnable data association module based on edge-augmented cross-attention, leveraging appearance and geometric features. Furthermore, we integrate this association module into the decoder layer of a DETR-based 3D detector, enabling simultaneous DETR-like query-to-image cross-attention for detection and query-to-query cross-attention for data association. By stacking these decoder layers, queries are refined for the detection and association task alternately, effectively harnessing the task dependencies. We evaluate our method on the nuScenes dataset and demonstrate the advantage of our approach compared to the two previous paradigms. Code is available at https://github.com/dsx0511/ADA-Track.