You are very close, and kudos for recognizing the hash of arrays (or more precisely, a hash of a hash of a hash of an array of hash references).

foreach iterates over a list, not a reference (see perlsyn). In this case, you need to dereference the array before foreach can use it.

foreach my $response ( @{ $content->{Addresses}{ArrayOfAddressResponse
+}{AddressResponse} } )
{
    # do something with $response, which is a hash ref
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