The only objective way for you to know if your employer values your skills is, if you get a raise and/or promotion. You have to understand the the first 12 months of any job is a review period. If you perform well and have the right attitude doing all of the jobs that no one else wants to do, then you can feel confident asking for an increase.
I would say that if you are working hard and contributing, as soon as you sense that you are not valued or respected, take the next opportunity as fast as you can. Sticking around and ‘learning more’ or in other words being ‘loyal’ is for mafia organizations that only know how to exploit their employees. You’ll know if the new opportunity provides a better environment to learn and build your skills. If it does…Take it, you are young.
A good career is made making opportunities for yourself and taking them when they present themselves to you. Sometimes you’ll have to wait a long period for the opportunity to present itself, sometimes it comes when you just got settled in a new city and you have to pour yourself into yet another vessel.
“You must be shapeless, formless, like water. When you pour water in a cup, it becomes the cup. When you pour water in a bottle, it becomes the bottle. When you pour water in a teapot, it becomes the teapot. Water can drip and it can crash. Become like water my friend.” -Bruce Lee
The only thing I will add to Mr. Lee is that it is only you who can and will decide if the current vessel form you are in is suitable.
Good luck…