If the part you want to keep starts at a fixed column then use substr to retrieve it:

#!/usr/bin/perl -w 
use strict;  
use warnings;
my $file = "./max/base/file.c:       \$(ROOT)/../../../api/maX  \\";

$file = substr $file, 25;
print "$file\n";
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Prints:

$(ROOT)/../../../api/maX  \
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Note in passing that you need to quote the $ for $(ROOT) in double quotes because Perl will see it as the special variable $( otherwise. If you actually wanted two \ characters at the end of the string you need to provide four ('\\\\') because \\ 'escapes' a \ and generates a single \ as a result.