ADD and ADHD are usually diagnosed more based on symptoms than any one particular thing. The testing that most Dr's give includes a parent evaluation, a teacher evaluation, and then another adult to answer the questions.
It is not uncommon at all for ADD/ADHD to have a component of LD, or be mistaken for LD. (NOW REMEMBER I'M OLD and a kid of the 70's).
In KG my teacher hated me because I was spaz, and couldn't sit still, talked too, much, did goofy things for no apparent reason, and she pegged me as dumb. (She was like 100 years old, and had been burned out for at least 50 of those years, not a pleasant lady).
1st grade rolls around, and by the middle of the 3rd week my teacher has me figured out. She was young, and had only been teaching for a year. She saw me chew a marker until it exploded, and got green ink all over my face, mouth, and hands. she saw me writing my letters backwards when they were mirrors of other letters bd pq etc. She called my parents, said I think little miss tush has ADD, and I was sent for real testing. Now back then only child psychiatrists did the evals, and he didn't even have to give me the full exam. He pegged me as ADD, and slightly dyslexic. He was awesome. They put me on Ritalin, and littl miss tush did much better all around.
Now the interesting thing was his philosophy wasn't to keep you on meds forever, just until you mature enough to learn coping stratagies, and methods to function, so I was off meds by middle school. When he signed off on me, he made a cassette tape for me to play when I was done with college or married. My mom gave it to me, then, I listened to it, and it was like the dude could see into the future. He really had me pegged, that I would struggle through school, and get average to slightly above average grades, and would excel at verbal things, that I would choose a carreer helping others, and not sit at a desk, that I would only have a handful of friends but those friends would be friends through thick and thin, and that my tolerance for bullshit would be very low. He nailed it.
I digressed a bit, but my point is without help kids with ADD/ADHD can really struggle, and with help and medication they can excel, and do well in life. Without can be very frustrated, and hate school, and tend to self medicate with drugs or alcohol.