Minimum wage is a wrong goal for people that wanna target the current work system. Wait. Sit tight and here me out on this.
THE FAILURE OF TRICKLE DOWN ECONOMY
The main problem in US economic system and in a lesser extent in all the other capitalist economies is a very uneven distribution of wealth. In the same production chain you can have a CEO amassing more money than some actual nations on Earth, more money than how 100 generations of people could actually spend in their entire lifetime, and workers at the bottom who struggle to survive.
Why is that so? How can it be possible for a successful and productive business capable of generating so much money to leave their workers at the base in worse conditions as days go by?
We can ironically point the finger at the failure of the trickle-down-economy philosophy, but the reality is that it was never applied. It could work theoretically but it has never been done. Money has never trickled down. Instead we have a black hole economy in which business owners exercise a gravitational pull which actually keeps all the money and avoid them to trickle down.
Trickle down economic idea is that if the system in its entirety grow in size, all that excess size can't be witholded by the upper level and will enrich all the steps of the pyramid. Instead what happens is that as more money they amass as more strong their gravitational pull get and always less wealth get distributed along the chain.
RAISING MINIMUM WAGES
Raising minimum wages won't solve this problem nor it will tackle this sick behavior in the economic system. You'll raise the wages to an acceptable minimum that will let you survive and hopefully live a decent life, but upper levels will keep exercising their gravitational pull. So they'll keep trying to get more excess wealth for themself and the easier way to do it will be raising prices.
So your new minimum wage will soon lose all its power in the upcoming inflation. We're not tackling the fact that we have access only to a small fraction of our productivity while few people take it all.
THE SOLUTION
What we need to do is tightly link upper level earnings to bottom level earnings. Like the highest paid man in a business can't bring it home more than 10x the lowest wage in the same business.
This way if a CEO wants a better salary then all the wages in the industry needs to go up. If a business goes well every worker must benefit from it. And the only way a manager can make millions is making the business successful. For everybody.