When you define $cmd as a string literal, you need to escape the backslashes, so you need to write:

my $cmd = "find $dir1 \\(! -name /proj/dev_dbdump/files_36  -prune\\) 
+-name $patt -print";
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You many also need to escape the search pattern, depending on what it is

Having said that, I think you would be better off investigating File::Find