void LL::DeleteLongest () {

 if (!head) return;
 int longest = head->longestlength();
 head = head->DelAllOfLength (longest);
}

int LLN::longestlength() {

 if (!next) return data.length();
 int lsf = next->longestlength();
 if (data.length() >= lsf) return data.length();
 return lsf;
}

LLN * LLN::DelAllOfLength (int n) {

 if (next) next = next->DelAllOfLength (n);
 if (data.length()==n) {
  LLN *t = next;
  next = nullptr;
  delete this;
  return t;
 }
 return this;
}

ALTERNATIVELY:

void LL::DeleteLongest () {

 if (!head) return;
 int longest = head->longestlength();
 head->DelAllOfLength (n);
 if (head->getdata().length()==longest) {
  LLN *t = head;
  head = t->getnext();
  t->setnext (nullptr);
  delete t;
 }
}

int LLN::longestlength() {

 if (!next) return data.length();
 int lsf = next->longestlength();
 if (data.length() >= lsf) return data.length();
 return lsf;
}

void LLN::DelAllOfLength (int n) {

 if (!next) return;
 next->DelAllOfLength (n);
 if (next->getdata().length()==n) {
  LLN *t = next;
  next = t->getnext();
  t->setnext (nullptr);
  delete t;
 }
}


Try this one:

void LL::MakeCircular ();

This attaches the tail node of the list to the head. The tail WAS pointing to null.  It should now point to the head.

If the list were A-->B-->C
it is now
A-->B-->C-->A-->B-->C-->A-->B-->C-->... forever ...

void LL::MakeCircular () {

 if (head)
  head->AttachToTail (head);
}

void LLN::AttachToTail (LLN *h) {

 if (next)
  next->AttachToTail (h);
 else
  next = h;
}