$dt->offset is giving you the +1100 and -0700 portion of each time format, but in seconds rather than hours, i.e. 11 hours = 39600 seconds and -7 hours = -25200 seconds. You could use the $dt->epoch method to get the duration in seconds:

my $duration = $dt_received->epoch - $dt_sent->epoch;
print "$duration seconds";

# 27 seconds
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For finer grained control of the result you can use subtract_datetime()

my $duration = $dt_received->subtract_datetime( $dt_sent );
print $duration->minutes, " minutes, ", $duration->seconds, " seconds"
+;

# 0 minutes, 27 seconds
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See DateTime::Duration