As one of the most common and abundant post-transcriptional modifications, N-methyladenosine (mA) has been extensively studied for its essential regulatory role in gene expression and cell functions. The location of mA RNA modification sites, however, remains a challenging problem, because of the inability to characterize mA modified sites at a multi-scale level in their native RNA context. Here, we introduce an interpretability-guided invertible neural network (mA-IIN), a deep learning model to accurately identify mA RNA modification sites by integrating both primary and secondary structure information under an invertible coupling framework. Compared to existing methods, mA-IIN achieves state-of-the-art performance in the prediction of mA RNA modification sites across 11 benchmark datasets collected from different species and tissues. Furthermore, we find evidence indicating high consistency in methylation-related regions between primary and secondary structure of RNA, providing novel insights into mA biology from the phylogenetic perspective. By analyzing conserved methylation-related regions identified by mA-IIN across tissues, mA-IIN facilitates the identification of novel pan-cancer genes, providing valuable contributions to cancer biology. Our results underscore the interpretability and predictive accuracy of mA-IIN, opening an avenue towards the understanding of mA RNA modification mechanisms.