You almost certainly can't combine the two lines in the way you probably want, where a request goes out one pipe/ISP and comes back in the other. The issue is your current ISP would need to be able to route your new IP block and that is highly unlikely.
What will probably be a better solution is to break requests out into services on different pipes or segment traffic based on IP. So you may send all web traffic to one pipe and all ftp traffic to another. That is actually not too hard to do with a CISCO router or any number of open source firewalls like Shorewall.
To be able to utilize the upload bandwidth from both your gateways you need to split the packets of the single upload connection to Youtube so that they will travel through both gateways, and then reassemble back into one connection to reach Youtube.
One way to do this is if your modem/router and your ISP support MLPPP.
But since most ISPs do not provide this there is another way (less stable/robust though on asynchronous gateways with unstable latency).
You will need a VPS server with 2 public IPs.
From your router you set up 2 VPN connections to the VPS.
Each connection will use each one of your gateways (hence the 2 public IPs on the VPS).
This can be done with simple static routes so that each IP is routed through each gateway.
Then you do bonding on top of those 2 VPNs to create a single link between your router and the VPS.
You then configure your router to route all packets from your LAN/PC via the bonding interface.
On the VPS side, you have to configure SNAT in order for the packets from the bonding interface to go out on the internet.
A crude diagram would be like this:
----- GATEWAY 1 -----
/ \
/ \
LAN/PC-------MODEM/ROUTER- - - BONDING - - -VPS SERVER------INTENRET
\ /
\ /
------ GATEWAY 2 ----
I have implemented the above using MikroTik RouterOS but it can be done on Linux too (since MikroTik is also Linux based).
For the bonding to work on top of the VPNs you will either need to use OpenVPN or EoIP (Ethernet over IP tunnel).
The bonding driver will be configured in balance-rr mode (Round Robin mode) so that the packets of a single connection will be split amongst the 2 VPNs.
The NAT needed is a simple masquerade only on the VPS to allow packets from your LAN/PC to go out on the internet with the VPS IP.
Best Answer
There are numerous appliances and routers (e.g. Zyxel P-663H) which will support two internet connections and balance outbound sessions across the two links.
For IP routing reasons this almost always involves NAT, although if you're already using NAT that shouldn't be an issue for you.
Balancing inbound traffic resiliently is a lot harder, since you have to publish an IP address for each inbound service, and those IPs can only ever be associated with one link.
The alternative is to swap to an ISP who can bond lines so that each line is properly bonded.