Step 1: Sort the four options into solid versus liquid media before choosing.
Step 2: LJ medium and Dorset medium are both coagulated egg based solid media, so they form slants rather than broths. Loeffler's serum slope is also a solid coagulated medium and is best known for diphtheria bacilli.
Step 3: That leaves MGIT, the Mycobacterial Growth Indicator Tube, which is a tube of modified Middlebrook 7H9 broth. Being a broth, it is the liquid medium requested.
Step 4: MGIT also speeds up TB detection because it is automated and reads growth through a fluorescence based oxygen sensor.
\[\boxed{\text{MGIT}}\]