If the fireplace hasn't been cleaned in years, dishwashing liquid probably won't be strong enough to remove the soot. Prep the area for cleaning and try a solution of dishwashing liquid ...

"Use a stiff-bristled brush to gently remove loose set from the bricks. Begin at the top of the fireplace ... notice soot buildup or dark discoloration on the bricks, it’s time to clean.

Limestone is often used for fireplace surrounds ... dirt, and soot. Additionally, consider doing a deep clean once or twice a year to get rid of any hard-to-remove dirt, debris, and staining ...