I have them taking the mold out however I feel its unsafe for me. Am i legally able to move out without breaking my rental contract?
The mold was caused by water.
Contracts / Agreements Lawyer
They should be providing you a proper home, consistent with the warranty of habitability. In this case a strong case can be made, I believe, for your Land Lord to pay for your stay at a hotel while the mold is being cleaned. If you wish to terminate the Lease agreement, that is another matter. It would likely have to be shown to still be unsafe to live there or that they did an inadequate job of cleaning the existing mold. It would also be helpful to find out how the mold got there in the first place.
Landlord / Tenant Lawyer
Every rental agreement, written or oral, contains an implied promise that the residence will be "habitable." "Habitable" doesn't mean "possible to live in," it means that the dwelling is basically safe and complies with health and safety standards. If your apartment is moldy (I'm not just talking about a little mildew in the shower here), then it is likely not waterproof--either there is a leak in the roof or in the plumbing that has not been fixed. Your landlord should find the source of the water and make the repair. If your landlord will not do so, then you are justified in moving out because your landlord will be in breach of the implied promise.
You might want to call the LAHD (866-557-RENT) and ask for a code enforcement inspection. The LAHD will not test for mold, but they might be able to tell if, for example, the walls are damp or the roof is leaking, and if so, order your landlord to make repairs.