The CPU can surehyl handle 10g of traffic per port un a DECENT card (note: you say nothing about brand - brand of the network card is VERY Important here). The question is whether it can PROCESS it, and that also depends on waht it does - even NGINX being efficient, 60g is a lot and 60g is - well, there is a difference between serving large static files and small requests. Can not be answered. But it is NOT A CPU I would buy for this area - I would go with something AMD EPYC based (tons of core, tons of IO).
THAT SAID: I would be very careful wit the data centers uplink (needs to be in the 100g area out of the rack minimum). I also dot nor eally understand the use of such a low end processor - the uplink and corresponding infrastructure will costs tens of thousands of dollars (because yes, you actually need to reserve 70-100, depending how much you accept as load factor, of external bandwidth from the data center and 10g backhauls will not be enough - things get EXPENSIVE at 100g).