Remotely sensed data are dominated by mixed land use and land cover (LULC) types. Spectral unmixing (SU) is a key technique that disentangles mixed pixels into constituent LULC types and their abundance fractions. While existing studies on deep learning (DL) for SU typically focus on single time-step hyperspectral or multispectral data, our work pioneers SU using MODIS MS time series, addressing missing data with end-to-end DL models. Our approach enhances a long-short-term-memory-based model by incorporating geographic, topographic (geo-topographic), and climatic ancillary information. Notably, our method eliminates the need for explicit endmember extraction, instead learning the input-output relationship between mixed spectra and LULC abundances through supervised learning. Experimental results demonstrate that integrating spectral-temporal input data with geo-topographic and climatic information significantly improves the estimation of LULC abundances in mixed pixels. To facilitate this study, we curated a novel labeled dataset for Andalusia (Spain) with monthly MODIS MS time series at 460-m resolution for 2013. Named Andalusia MultiSpectral MultiTemporal Unmixing, this dataset provides pixel-level annotations of LULC abundances along with ancillary information.