Recent advances in speech enhancement have shown that models combining Mamba and attention mechanisms yield superior cross-corpus generalization performance. At the same time, integrating Mamba in a U-Net structure has yielded state-of-the-art enhancement performance, while reducing both model size and computational complexity. Inspired by these insights, we propose RWSA-MambaUNet, a novel and efficient hybrid model combining Mamba and multi-head attention in a U-Net structure for improved cross-corpus performance. Resolution-wise shared attention (RWSA) refers to layerwise attention-sharing across corresponding time- and frequency resolutions. Our best-performing RWSA-MambaUNet model achieves state-of-the-art generalization performance on two out-of-domain test sets. Notably, our smallest model surpasses all baselines on the out-of-domain DNS 2020 test set in terms of PESQ, SSNR, and ESTOI, and on the out-of-domain EARS-WHAM_v2 test set in terms of SSNR, ESTOI, and SI-SDR, while using less than half the model parameters and a fraction of the FLOPs.