RNA modifications such as m6A methylation form an additional layer of complexity in the transcriptome. Nanopore direct RNA sequencing can capture this information in the raw current signal for each RNA molecule, enabling the detection of RNA modifications using supervised machine learning. However, experimental approaches provide only site-level training data, whereas the modification status for each single RNA molecule is missing. Here we present m6Anet, a neural-network-based method that leverages the multiple instance learning framework to specifically handle missing read-level modification labels in site-level training data. m6Anet outperforms existing computational methods, shows similar accuracy as experimental approaches, and generalizes with high accuracy to different cell lines and species without retraining model parameters. In addition, we demonstrate that m6Anet captures the underlying read-level stoichiometry, which can be used to approximate differences in modification rates. Overall, m6Anet offers a tool to capture the transcriptome-wide identification and quantification of m6A from a single run of direct RNA sequencing.