It's quite annoying that we can't edit our posts any more, I came back to do this to my egregious advice:
I vaguely recalled seeing 15v on the datasheet of the chip... checking ...
LF353 can have a supply voltage of 18v — so long as you've got caps rated for 50v or more, you're good to go.
I think.
I'll defer to the experts.
Edit: LF, not LM...