<p>This paper studies a class of distributed aggregative optimization problems over unbalanced directed graphs, a setting where the local objective of each agent depends on both its individual decision variables and an aggregate of all agents states. To efficiently solve this problem, we propose a novel algorithm that integrates a unified momentum technique with distributed aggregative gradient tracking. A key element of the design is the introduction of an auxiliary variable to estimate the left Perron eigenvector of row-stochastic matrices, enabling effective handling of network imbalance. We provide a rigorous theoretical analysis, proving that the proposed algorithm achieves linear convergence when parameters are selected within specified ranges. Extensive numerical experiments are conducted, and the results demonstrate the superior computational efficiency of our method compared to existing state-of-the-art approaches.</p>