Reading contents of a file based on character position

If I have a file with the sentence:

I like apples and oranges   
but I hate broccoli

How would I go about storing to a variable the following string from the file:

ut I hate broc

I have tried using mycut=$(cut -c 2-15 file), but this cuts from both lines in the file (mycut == "I like apples a ut I hate broc"). I only want to grab the string those specific character positions from that specific line. Is there some way I can do this?

If there is a better way other than using cut, that's fine too.