I think you're asking the wrong question. But here goes...
Quick math: If the other job is 50 miles further away, and your car gets 25 miles to a gallon, it'll take you 4 gallons of gas per day to commute the difference in the distance between the two jobs. At $2.25 per gallon, buying 4 gallons of gas, working 250 days per year, it will cost you $2250 more in gas alone, just to commute. Assuming your $6K will be taxed at a "marginal" tax rate of about 40%, you really are only getting $3600 more (take home).
So the far away job is going to be worth about $1350 per year (which is $3600 minus the gas costs), which is nowhere near the cost of a car (payments, insurance, maintenance, etc). (Not to mention the stress of that much driving!)
Not sure if my assumptions are correct, but that should give you a mathematical way to look at it. Basically, if my assumptions are correct, you should NOT take this job if you are looking for short-term financial gains.
HOWEVER, like I said, you are asking the wrong question.
If the current job is truly "dead end", then it's time to look elsewhere. You really need to be looking out for the next 5 years when it comes to a job. And remember, this is NOT a decision between just these TWO jobs... there are a lot of jobs out there, and I'm sure that there are non-dead-end jobs that are closer to home.
What you should do is to evaluate what an ideal job looks like that you are qualified for. I think that being close to home should be one criteria (especially if transportation is an issue). But look for something that has a 5-year possibility of growth. Not that you need to be CEO in 5 years, but can you grow, and increase pay, and learn and be positioned for an even better job?
Then conduct an aggressive, thorough job search. That could be the subject of another question. But you want to be in a position where you are deciding between two or three GREAT jobs, and then you're doing it right!
No dead end jobs. Ever.