People who suffer from hearing impairments can find it difficult to follow a conversation in a multi-speaker environment. Modern hearing aids can suppress background noise; however, there is little that can be done to help a user attend to a single conversation without knowing which speaker is being attended to. Cognitively controlled hearing aids that use auditory attention decoding (AAD) methods are the next step in offering help. A number of challenges exist, including the lack of access to the clean sound sources in the environment with which to compare with the neural signals. We propose a novel framework that combines single-channel speech separation algorithms with AAD. We present an end-to-end system that 1) receives a single audio channel containing a mixture of speakers that is heard by a listener along with the listener's neural signals, 2) automatically separates the individual speakers in the mixture, 3) determines the attended speaker, and 4) amplifies the attended speaker's voice to assist the listener. Using invasive electrophysiology recordings, our system is able to decode the attention of a subject and detect switches in attention using only the mixed audio. We also identified the regions of the auditory cortex that contribute to AAD. Our quality assessment of the modified audio demonstrates a significant improvement in both subjective and objective speech quality measures. Our novel framework for AAD bridges the gap between the most recent advancements in speech processing technologies and speech prosthesis research and moves us closer to the development of cognitively controlled hearing aids.