It's not true that it takes 30 carrots to make 2/3 cup of grated carrots, but it FEELS true. Actually it takes 2 carrots and 2 bandaids if you use a box grater.
These days I put carrots in the juicer (for making carrot vinegar) and use the pulp for carrot cake, freezing most of it. It's quite fine so the cake is smoother, though you still get most of the carrot crunch, just not as many carrot pieces stuck between your teeth.
I like raisins in carrot cake but not nuts.