In recent years, deep neural networks, including Convolutional Neural Networks, Transformers, and State Space Models, have achieved significant progress in Remote Sensing Image (RSI) Super-Resolution (SR). However, existing SR methods typically overlook the complementary relationship between global and local dependencies. These methods either focus on capturing local information or prioritize global information, which results in models that are unable to effectively capture both global and local features simultaneously. Moreover, their computational cost becomes prohibitive when applied to large-scale RSIs. To address these challenges, we introduce the novel application of Receptance Weighted Key Value (RWKV) to RSI-SR, which captures longrange dependencies with linear complexity. To simultaneously model global and local features, we propose the Global-Detail dual-branch structure, GDSR, which performs SR by paralleling RWKV and convolutional operations to handle large-scale RSIs. Furthermore, we introduce the Global-Detail Reconstruction Module (GDRM) as an intermediary between the two branches to bridge their complementary roles. In addition, we propose the Dual-Group Multi-Scale Wavelet Loss, a wavelet-domain constraint mechanism via dual-group subband strategy and cross-resolution frequency alignment for enhanced reconstruction fidelity in RSI-SR. Extensive experiments under two degradation methods on several benchmarks, including AID, UCMerced, and RSSRD-QH, demonstrate that GSDR outperforms the state-of-the-art Transformer-based method HAT by an average of 0.09 dB in PSNR, while using only 63% of its parameters and 51% of its FLOPs, achieving an inference speed 3.2 times faster.