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Bandwidth forecasting in Mobile Broadband (MBB) networks is a challenging task, particularly when coupled with a degree of mobility. In this work, we introduce HINDSIGHT++, an open-source R-based framework for bandwidth forecasting experimentation in MBB networks with Long Short Term Memory (LSTM) networks. We instrument HINDSIGHT++ following an Automated Machine Learning (AutoML) paradigm to first, alleviate the burden of data preprocessing, and second, enhance performance related aspects. We primarily focus on bandwidth forecasting for Fifth Generation (5G) networks. In particular, we leverage 5Gophers, the first open-source attempt to measure network performance on operational 5G networks in the US. We further explore the LSTM performance boundaries on Fourth Generation (4G) commercial settings using NYU-METS, an open-source dataset comprising of hundreds of bandwidth traces spanning different mobility scenarios. Our study aims to investigate the impact of hyperparameter optimization on achieving state-of-the-art performance and beyond. Results highlight its significance under 5G scenarios showing an average Mean Absolute Error (MAE) decrease of near 30% when compared to prior state-of-the-art values. Due to its universal design, we argue that HINDSIGHT++ can serve as a handy software tool for a multitude of applications in other scientific fields.