Left-brain/right-brain have nothing to do with spirituality.
Although, researchers have found a small portion of the right-brain, that when stimulated, gives a feeling of comfort, euphoria, and a sense of 'something powerful' nearby and a 'oneness with the universe' that many claim is communion with god. It seems our brains are wired to trick us into believing. Why do we need this part of our brain? Because once we evolved a sense of our own mortality, we developed a great deal of anxiety, which can be distracting when hunting/trying to survive. A feeling of well-being helps eliminate that feeling.