This sounds like an apache related problem (since you seem to have defined your route correctly).
My first to checks here would be:
Is mod_rewrite enabled? Without this your .htaccess won't be used.
Are you allowing rewrites within your virtual host declarations and in your config? (Sorry you didn't mention how well you know apache).
Are your laravel folder permissions correctly set? (See https://laravel.com/docs/5.2/installation in the section on directory permissions). [I circumvented this problem by changing my apache user to match my user - but probably wouldn't do this in production].
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