This is a 6 to 8 days, depending on your fitness and wishes, trek, or rather a small expedition to climb up 4600m. to Dzongri view point and then up to 5400m. to the Goecha La pass, right under the mighty Kanchenjunga.
There is absolutely no guesthouses on the road (only a few trekker's huts) so you need tents, a kitchen, a supply of food for a whole week, a cook, porters, horses and sometimes even yaks to carry all your camping equipment. This means that the bigger the group - the better, but, of course, it is possible to go even alone - that just will cost you substantially more (you have to pay to all the staff).
There are rules, everywhere in Sikkim or West Bengal, that you cannot go alone into any national park or restricted area. You have to hire a local guide and obtain appropriate permits. Occasionally, you could see some punks on the trail, but if caught, especially in restricted North Sikkim, they could end up in an Indian military prison - no jokes.
For this trek the base camp is a beautiful Yuksom village - the first capital of Sikkim, they say. It is surrounded by green hills from each side, but south, so it has a unique, very mild micro climate - mostly sunny and warm. In Yuksam there are lots of small trekking agencies which could organize everything.
The Glacier Trek & Adventure of mr.Kiran Gurung in Yuksom - the Goecha La specialist, and the Sikkim Holidays of mr. Barap Bhutia in Gangtok, who specializes in North Sikkim, both are my long time friends. I had my first serious trekking with them back in 2008.
My pictures from