You may be missing the forest for the trees. Or in this case, for the mountains.
Human geography is influenced hugely by physical geography and economics. Mountains do a good job of inhibiting the flow of people, and thus cultures on either side of a mountain range are often distinct. Of course if you're someone who lives on the mountain, and thus navigates along it, not the same dynamic. But in this case specifically we are talking about the Himalayas; the greatest mountain range in the world.
There are very few places where you can cross directly from India into China, and these appearare exclusively for Indian pilgrims to visit holy sites across the border (like Mount Kailash). China opened a road thereabouts in June 2015.
If you want to drive from Delhi to Beijing, you'd have to travel through Nepal or Pakistan. Nepal's Araniko Highway meets China's National Highway 318. Pakistan's Karakoram Highway (N-35) meets China's National Highway 314. This will be somewhat bothersome, and there'd certainly be plenty of paperwork and delays along the way. After crossing into China you'd have arrived on the Tibetan Plateau, a vast and unforgiving high altitude wilderness.
So there's easier ways to get to China, like a boat or a plane. But why would someone go?
If you can afford a good education and a plane ticket, you're going to want to go to a country where you can maximise your earnings. Consequently rich Indians aren't likely to go to China, where wages are lower than the developed world.
Poor Indians are either going to travel to neighbouring countries to sell their labour, or richer countries will pay to transport them for their cheap labour; most notably Saudi Arabia and the Gulf States. Considering that travel to China requires passage through Nepal or Pakistan with paperwork a necessity, for poor Indians the cost of the adventure would be too much.
It should be little surprise that the Indian diaspora is spread most thickly around India's neighbours, and the most affluent English-speaking nations. The Gulf states are an obvious exception.
Beyond this, it's worth noting that China has its own enormous population. Consequently, even if Chinese wages were significantly high, China would unlikely have labour shortages, like those faced by developed nations and the Gulf states.
To summarise: Given geography it is too expensive for poor Indians to travel to China. There's also no need for China to import cheap labour from India, China has plenty of its own. For rich Indians who can afford to travel long distances, there are other places to move for skilled employment which will allow them to earn more money than China.