I am 5'11" and used to be 135 pounds. I'm now 160. I look slim, but toned and not rail thin. Most people here might not be impressed but I look and feel a lot better. I don't necessarily advocate my routine or diet because I'm not an expert, and people have probably rightly criticized it. But I'll share what I've done:
Breakfast (2 eggs, toast and peanut butter, banana, protein shake)
Lunch: Sand which, raw vegetables
Snacks at work: Apple, peanuts, wheat crackers
Dinner: Basically meat, potato, vegetable.
I lift Tues, Thurs, Sat, and Sun. I lift 30 minutes for sure on Tues and thurs, but on weekend I sometimes go for an hour. I have to watch my back though so I don't really push too hard. Other days I run or jump rope.
Some of the foods I just eat because I like them. My goal was never get to huge, but just not look weak and thin.
Lifting, protein shake, more snacks, and bigger breakfast helped. The bigger breakfast makes me feel better mentally in the morning. I like snacking during work because it helps me get through the day.
One problem I've had is, like you, I'm never rarely ever hungry. I would be fine with never snacking. If I eat too much at a meal, I get a stomach ache. So I try to eat snacks. But even though I get sick if I eat too much. I've tried adding peanut butter to the protein shakes. Some people say the shakes aren't good for you, but I feel that they helped me.